Stability and control of a compass gait model walking with series-elastic ankle actuation
Passive dynamic walking models are capable of capturing basic properties of walking behaviors and can generate stable human-like walking without any actuation on downhill surfaces. The passive compass gait model is among the simplest of such models, consisting of a planar point mass and two stick legs. A number of di erent actuation methods have been proposed both for this model and its more complex extensions to eliminate the need for a downhill sloped ground, balancing collision losses using gravitational potential energy. In this thesis, we introduce and investigate an extended compass gait model with series-elastic actuation at the ankle towards a similar goal, realizing stable walking on various terrains such as level ground, inclined surfaces and rough terrains. Our model seeks to capture the basic structure of how humans utilize toe push-o prior to leg lifto , and is intended to eventually be used for controlling the ankle joint in a lower-body robotic orthosis. We derive hybrid equations of motion for this model and obtain limit cycle walking on level and inclined grounds. We then numerically identify xed points of this system and and show numerically through Poincar e analysis that it can achieve asymptotically stable walking on level and inclined ground for certain choices of system parameters. The dependence of limit cycles and their stability on system parameters such as spring precompression and sti ness for level ground walking is identi ed by studying the bifurcation regimes of period doubling of this model, leading to chaotic walking patterns. We show that feedback control on the initial extension of the series ankle spring can be used to improve and extend system stability on level ground walking. Then, we investigate and identify the period doubling bifurcation regions of our model for spring precompression and ground slope parameter leading to various maps that we utilize for rough terrainwalking. Furthermore, we evaluate the performance of our model on rough terrains by applying ground slope feedback controllers on the spring precompression. Thereafter, we demonstrate that slope feedback along with stance leg apex velocity feedback control on the extension of the series ankle spring improves walking performance on rough terrains. The implementation of series elastic actuation on the ankle joint is realized with an experimental instantiations of active ankle foot orthosis system for the patients walking unnaturally and ine ciently with impaired ankles. Finally, we integrate the active ankle foot orthosis platform with an active knee orthosis platform where the experimentation results indicate that the integrated platform can generate e cient walking patterns.